Private information and its effect on market equilibrium: New evidence from long-term care insurance

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1 Private information and its effect on market equilibrium: New evidence from long-term care insurance Amy Finkelstein Harvard University and NBER Kathleen McGarry University of California, Los Angeles and NBER August 2003 This paper examines the standard test for asymmetric information in insurance markets: that its presence will result in a positive correlation between insurance coverage and risk occurrence. We show empirically that while there is no evidence of this positive correlation in the long-term care insurance market, asymmetric information still exists. We use individuals subjective assessments of the chance they will enter a nursing home, together with the insurance companies own assessment, to show that individuals do have private information about their risk type. Moreover, this private information is positively correlated with insurance coverage. We reconcile this direct evidence of asymmetric information with the lack of a positive correlation between insurance coverage and risk occurrence by demonstrating the existence of other unobserved characteristics that are positively related to coverage and negatively related to risk occurrence. Specifically, we find that more cautious individuals are both more likely to have longterm care insurance and less likely to enter a nursing home. Our results demonstrate that insurance markets may suffer from asymmetric information, and its negative efficiency consequences, even if those with more insurance are not higher risk. The results also suggest an alternative approach to testing for asymmetric information in insurance markets. Key Words: asymmetric information; long-term care insurance JEL classification: D82, G22, I11 We thank Daron Acemoglu, Jeff Brown, Pierre-Andre Chiappori, Raj Chetty, Janet Currie, David de Meza, Seema Jayachandran, Jerry Hausman, Ginger Jin, Larry Katz, Ben Olken, Sarah Reber, Casey Rothschild, Michael Rothschild, Bernard Salanie, Jesse Shapiro, Jonathan Wright, and seminar participants at Berkeley, Stanford, San Diego, the University of Chicago, and the NBER Summer Institute for helpful comments and discussions. We are especially grateful to the employees of the insurance company who generously provided us with the proprietary data used in this paper and answered many questions about it, and to Jim Robinson for generously providing us with the actuarial model of long-term care utilization. We thank the NBER and NIA for financial support.

2 Theoretical research has long emphasized the potential importance of asymmetric information in impairing the functioning of insurance markets. Its empirical relevance, however, remains the subject of considerable debate. 1 Several recent studies of the automobile, health, and life insurance markets have concluded that asymmetric information does not exist in these insurance markets (e.g. Chiappori and Salanie, 2000; Cardon and Hendel, 2001; and Cawley and Philipson, 1999). These studies are all based on the same widely used test of asymmetric information: they test for whether there is a positive correlation between insurance coverage and risk occurrence. Contrary to the predictions of many moral hazard and adverse selection models, these papers find no evidence that individuals with more insurance are more likely to experience the insured risk. These findings have challenged the conventional wisdom that asymmetric information is an important phenomenon in insurance markets. In this paper, we show empirically that asymmetric information may exist in an insurance market even when the expected positive correlation between insurance coverage and risk fails to materialize. Individuals may have private information not only about their risk type but also about preference-related characteristics (such as risk aversion). If these unobserved preference-related characteristics have the opposite correlation with insurance coverage and with risk occurrence, they may offset the positive correlation between insurance coverage and risk occurrence that private information about risk type would otherwise produce. Thus, rather than indicating symmetric information, the lack of a positive correlation between insurance coverage and risk occurrence may indicate that there exist multiple forms of private information, acting in different directions. Distinguishing between these two explanations for the same observed equilibrium is critical to understanding the information structure of the market. It also has important implications for efficiency. A symmetric information explanation indicates that there are no information-based efficiency problems. In contrast, an explanation based on multiple forms of private information raises the possibility that the 1 Indeed, even when awarding the 2001 Nobel prize for the pioneering theoretical work on asymmetric information, the Nobel committee noted in its extended citation that empirical evidence of asymmetric information in insurance markets was ambiguous (Bank of Sweden, 2001). 1

3 structure of information may create market inefficiencies. Despite the importance of distinguishing between these two very different explanations for a lack of a positive correlation between insurance coverage and risk occurrence, there have been no empirical tests designed to do so. We provide one here. While the ideas advanced in this paper are applicable to a wide variety of insurance markets, we focus our empirical work on the private long-term care insurance market in the United States. In addition to providing an interesting setting for studying asymmetric information, this market is of substantial importance in its own right. With annual expenditures of $100 billion (over 40 percent of which are paid for out of pocket) long-term care expenditures currently represent one of the largest uninsured medical and financial risks faced by the elderly in the United States. As the baby boom generation ages and medical costs rise, the nature of the long-term care insurance market will have profound implications for the well-being of both the elderly and their children. The limited size of the long-term care insurance market is well-known, but not well understood. Adverse selection and moral hazard may play a role, yet there exists little empirical evidence on their existence in this market. We begin by following the existing literature and examine whether there is a positive correlation between the amount of insurance individuals have and the occurrence of the risk (in this case, the individual s ex-post use of a nursing home). We analyze data from two complementary sources: proprietary micro data from a large private long-term care insurance company, and individual-level panel data from the Asset and Health Dynamics of the Oldest Old (AHEAD) cohort of the Health and Retirement Survey (HRS). We find no evidence that, after controlling for the risk classification done by the insurance company, those with more long-term care insurance use more nursing home care. If anything, we find suggestive evidence that they use less nursing home care. To distinguish whether this equilibrium reflects the presence of symmetric or asymmetric information, we directly examine whether individuals have private information about their risk type. In the AHEAD data, we can measure each individual s subjective belief of his probability of entering a nursing home over the next five years, and compare that prediction to his subsequent five-year nursing home utilization. We supplement these data with measures of the insurance companies information set 2

4 and risk classification practices; these measures are based on insurance company application forms which reveal the set of individual characteristics observed by the insurance companies, and on the industry s actuarial model of nursing home utilization as a function of these observed characteristics. We find that, after controlling for the insurance company s risk-classification, the individual s beliefs about his subsequent nursing home use remain a positive and statistically significant predictor of subsequent nursing home use. This test provides direct evidence of asymmetric information in the private long-term care insurance market: individuals have information about the likelihood of risk occurrence that the insurance company does not. Moreover, we find that the individual s private information about his risk type is positively correlated with insurance coverage. These results together with our failure to find a positive correlation between nursing home utilization and long-term care insurance coverage suggest the existence of unobserved heterogeneity not only in risk type but also in preferences, where some preferences have the opposite correlation with insurance coverage and with nursing home utilization, and thus mask the role of adverse selection and moral hazard. Indeed, we demonstrate that, in the absence of this offsetting preference-based selection, the typical individual with long-term care insurance would be of substantially higher risk than an individual without such coverage. We also provide direct evidence of the existence and nature of these other unobserved, preference-related characteristics. Consistent with the theoretical models of de Meza and Webb (2001) and Jullien et al. (2002), we find that more cautious individuals (a characteristic not observed by the insurance companies) are both more likely to own long-term care insurance and less likely to end up using long-term care. The rest of the paper is structured as follows. Section one describes the standard empirical test for whether insurance coverage and risk occurrence are positively correlated and discusses different possible explanations for a lack of a positive correlation; we emphasize their different implications for the structure of information and for market efficiency. Section two provides some brief background on the private long-term care insurance market. The next three sections present the three main empirical findings. Section three documents the lack of a positive correlation between long-term care insurance 3

5 coverage and nursing home care utilization. Section four provides evidence that individuals have private information about their risk type and shows the impact of this private information on insurance coverage and on the market equilibrium. Section five investigates the nature of the other offsetting, unobserved factors. The final section summarizes our findings. We discuss their potential to help reconcile the existing evidence of differences across insurance markets in whether there is a positive correlation between insurance coverage and risk occurrence, and their implications for testing for asymmetric information in other insurance markets. 1. Theoretical background 1.1 The positive correlation prediction A wide variety of asymmetric information models predict a positive correlation between the amount of insurance and the occurrence of the risky event (Chiappori and Salanie, 2000; Chiappori et al., 2002). As a result, the standard test for asymmetric information has been a test of the correlation between the amount of insurance coverage and the ex-post occurrence of the (potentially) insured risk. Throughout the paper we will refer to this test as the positive correlation prediction. 2 The positive correlation can arise from either adverse selection or moral hazard, both of which result in a market that is inefficient relative to the first best. The mechanism by which the positive correlation arises differs however, for the two phenomena. In the case of adverse selection, the insured is assumed to have ex-ante superior information to the insurance company about his risk type. Because individuals who appear to the insurance company to be observationally equivalent face the same menu of insurance options, and because the marginal utility of insurance at a given price is increasing in risk, those with private information that they are high risk will select contracts with more insurance than those with private information that they are low risk (see e.g. Rothschild and Stiglitz, 1976). In the case of moral 2 Of course, this prediction applies only to individuals who would be treated symmetrically by the insurance company (i.e. placed in the same risk category and offered the same set of insurance contract options). Although we will not always state this qualification explicitly in our discussion, it is implicitly always present. In the empirical work below, we will take great care to condition on this risk classification. 4

6 hazard, the causality is reversed and the informational asymmetry occurs ex-post: insurance coverage lowers the cost of an adverse outcome and thus increases the probability or magnitude of the risk occurrence. The classic explanation is that insurance reduces the individual s incentive to invest in (costly) risk-reducing effort (see e.g. Arnott and Stiglitz, 1988). In the health insurance context, another form of moral hazard may be quantitatively more important: insurance lowers the marginal cost of consuming the insured good (medical care), and may therefore induce additional consumption. Empirically, the positive correlation property appears to exist in some insurance markets but not others. Cutler (2002) reviews an extensive empirical literature that finds evidence of the positive correlation property in health insurance, although exceptions exist (e.g. Cardon and Hendel, 2001). There is also evidence from annuity markets that the insured are higher risk (Finkelstein and Poterba, 2002, forthcoming), but no such evidence in life insurance markets (Cawley and Philipson, 1999). In the automobile insurance market, the empirical evidence is mixed. Chiappori and Salanie (2000) and Dionne et al. (2001) fail to reject the null hypothesis of no correlation; but Pueltz and Snow (1994) and Cohen (2001) find support for the positive correlation prediction. 1.2 Implications for the structure of information and market efficiency There are two broad classes of possible explanations for a lack of a positive correlation between insurance coverage and risk occurrence. One argues that there is symmetric information, while the other argues that there is asymmetric information about both risk type and preferences, and that the two effects offset each other. Here, we provide an intuitive discussion of the two scenarios, and their efficiency implications. Interested readers should consult Chiappori et al. (2002) for a more formal discussion. 3 Consider first the possibility that information is symmetric and there is no moral hazard. Given the vast amount of information that insurance companies can, and do collect about potential customers, the individual may not have residual private information; indeed sophisticated actuarial methods might even 3 Chiappori et al. (2002) show not only that asymmetric information may exist in the absence of a positive correlation (which is the possibility we focus on here), but also that asymmetric information may not exist even with a positive correlation. 5

7 give the insurance company superior information about the individual s risk type. 4 It is also possible that moral hazard may not exist in particular insurance markets. For example, in the case of long-term care insurance, the unappealing nature of nursing homes may be sufficient to dampen any potential moral hazard effects. If individuals have no private information and there is no moral hazard, insurance coverage need not be positively correlated with risk occurrence. Moreover, with symmetric information, the structure of information will not distort insurance purchases; the equilibrium will therefore be first best (absent any other market imperfections). An alternative explanation for a lack of a positive correlation between insurance coverage and risk occurrence is that unlike in the standard models of asymmetric information risk type may not be the only source of private information. Individuals may also differ with respect to unobserved preferences such as risk aversion that are correlated with both the demand for insurance coverage and with risk occurrence. We refer to this as preference-based selection to distinguish it from traditional adverse (or risk-based ) selection derived solely from the individual s private information about his risk type. If unobserved preferences are positively correlated with insurance demand and negatively correlated with risk occurrence, they can offset, to some degree, the positive correlation between insurance and risk occurrence that adverse selection and moral hazard would otherwise produce. The correlation between insurance and risk occurrence may therefore be of indeterminate sign. For example, more risk averse individuals value insurance more; if they are also lower risk perhaps because they invest more in riskreducing effort the correlation between insurance coverage and risk occurrence may be positive, zero or even negative (Jullien et al., 2002, de Meza and Webb, 2001). 5 4 In this case, the equilibrium may exhibit a negative correlation between insurance coverage and risk occurrence (Villeneuve 2000, Villeneuve forthcoming). 5 It should be noted that when there is private information about risk type, unobserved preference heterogeneity is not sufficient to generate a zero or negative correlation between insurance coverage and risk occurrence; it is also necessary that there be some sort of markup above expected claims, due either to imperfect competition or a marginal production cost. In other words, as long as there is perfect competition and no loading, the standard positive correlation test for asymmetric information will still be valid, even in the presence of unobserved preference heterogeneity (Chiappori et al, 2002). 6

8 We emphasize that the presence of private information about risk type may preclude an efficient equilibrium, even if, due to the presence of offsetting preference-based heterogeneity, the positive correlation property does not obtain. This theoretical result has been shown formally by Jullien et al. (2002) for the specific case of a monopoly insurance provider, along with private information about risk preferences and risk type, and endogenous risk probabilities. De Meza and Webb (2001) establish a similar result for a competitive insurance market with administrative costs. Some of the intuition behind these results for why the market is inefficient can be demonstrated with a simple example. Consider the case in which private information about risk type and offsetting preference-based selection produce an equilibrium with no correlation between insurance coverage and risk occurrence. There are therefore two groups of individuals purchasing a given insurance policy: low risk, high risk aversion individuals, and high risk, low risk aversion individuals. Because these groups pay the same price for the insurance policy, but have different expected costs, it cannot be the case that both groups are paying an actuarially fair price, and the quantity of insurance purchased by at least one group will therefore not be first best. In general, with private information about risk type and risk preferences, the direction of the inefficiency is unclear; insurance coverage may either be higher or lower than the first best outcome. In addition, there may or may not be scope for Pareto-improving government intervention. 6 Finally, we note that it is not, in general, possible to draw comparisons of the relative efficiencies of alternative equilibria based on the observed correlation between insurance coverage and risk occurrence. A change in the structure of preferences across individuals of different risk types could produce a change in this correlation, but with changes in preferences, efficiency comparisons are not straightforward. Moreover, a change in the correlation likely involves increases in insurance for some risk types and decreases for other, making the net change in efficiency unclear. This indeterminacy is important to keep 6 Even in standard asymmetric information models in which individuals only differ in terms of their (privately known) risk type there is variation across models in whether there is scope for Pareto improving government intervention (Crocker and Snow, 1985). The same is true in models with private information about both risk type and risk preferences. For an example of a model with private information about both risk type and risk preferences in which some individuals have too much insurance relative to the social optimum and there is scope for Pareto improvement through government intervention, see de Meza and Webb (2001). 7

9 in mind. Later in the paper, we show that in the absence of preference-based selection, those with longterm care insurance would on average be substantially higher risk than those without insurance. However, we caution that this result does not by itself imply that the resulting equilibrium would be more (or less) efficient absent preference-based heterogeneity. 2. Background on long-term care and long-term care insurance At almost $100 billion a year in 2000, long-term care expenditures in the United States comprise 7.5% of total health expenditures for all ages, and about 1% of GDP. There is substantial variation among the elderly in their long-term care utilization; for example, Dick et al. (1994) estimate that while two-thirds of individuals who reach age 65 will never enter a nursing home, one-quarter of women who do enter a nursing home will spend at least three years there. This suggests potentially large welfare gains from insurance coverage that reduces this expenditure risk. However, most of this substantial expenditure risk is currently uninsured. Over 40 percent of longterm care expenditures for the elderly are paid for out of pocket, compared to only 17 percent of the elderly s expenditures in the health sector as a whole (US Congress, 2000, National Center for Health Statistics, 2002). This disparity partly reflects the limited public insurance coverage for long-term care. Medicare, the public health insurance program for the elderly, covers only a very restricted set of longterm care services. Medicaid, the public health insurance program for the indigent, is available only to elderly individuals with little or no wealth and very low disposable income. The extremely limited nature of private long-term care insurance coverage is also an important factor. We estimate that in the 2000 HRS, only 10 percent of those aged 65 and over had private long-term care insurance coverage. Moreover, most private insurance policies insure only a limited fraction of long-term care expenditures. Policies often have daily and lifetime benefit caps and are typically not indexed for inflation. Brown and Finkelstein (2003) estimate that typical private policies pay for less than 50 percent of the expected present discounted value of long-term care costs for a 65 year old. As a result, private 8

10 insurance covers only about 5 percent of the elderly s long-term care expenditures, compared to 35 percent of the elderly s overall health expenditures (US Congress, 2000, National Center for Health Statistics, 2002). About 80 percent of private long term care insurance is provided by the individual (non-group) market (HIAA 2000b). The average age of purchase in this market is 67. Coverage rates are roughly comparable for men and women. However, they increase substantially with asset levels, probably due, at least in part, to the means-tested nature of Medicaid (HIAA, 2000a). Firms use relatively little information specific to the individual in pricing these policies, despite the absence of regulatory restrictions. Policies are not experience rated. Premiums tend to vary only with age at purchase, and with several broad health categories (ACLI, 2001; Weiss 2002). Premiums do not vary by gender. 7 A variety of theoretical explanations have been proposed for the limited size of the private long-term care insurance market (see Norton, 2000 for a review). Asymmetric information is one potential explanation, yet there exists very little empirical evidence on its presence in this market. Consistent with moral hazard, Garber and MaCurdy (1993) present evidence of an increase in nursing home discharges when the Medicare nursing home benefit is exhausted. The widespread use of deductibles in long-term care insurance policies (Brown and Finkelstein, 2003) is also suggestive of asymmetric information. 3. Is there a positive correlation between LTC coverage and care use? Long-term care includes both care in a nursing home and home health care. Nursing homes are substantially more expensive than home health care (MetLife 2002), and account for over three-quarters of long-term care expenditures (US Congress, 2000). Moreover, until quite recently, long term care 7 This unisex pricing practice may initially seem quite puzzling, since women use substantially more long-term care than men (Society of Actuaries, 1992). However, using the data in Section 3, we find that gender is no longer a substantively or statistically significant predictor of nursing home use after conditioning on the age and healthrelated rate classification employed by the insurance company. Thus it appears that through the use of health-related categories, insurance companies can capture all of the risk-related information contained in gender. Consistent with this, we do not find any differences across gender in insurance coverage. Presumably the insurance companies find this a more politically attractive alternative to pricing directly based on gender. 9

11 policies tended to cover only nursing home care. 8 Because of these patterns, and data limitations discussed below, our empirical analysis focuses primarily on the relationship between insurance coverage and nursing home utilization. Figure 1 based on aggregate data from the Society of Actuaries (SOA, 2002) shows the ratio of nursing home admission rates for insured individuals to admission rates for the general population, by age and by sex. 9 The positive correlation property predicts that the insured-to-population ratio of admission rates should be larger than one. The pattern displayed in Figure 1 is not consistent with this prediction. We observe similar admission rates for the insured relative to the population at younger ages, and much lower nursing home admission rates for the insured relative to the population at older ages. The SOA (2002) also provides data on the relative nursing home admission rates, by age, among insured individuals with varying amounts of insurance. Again there is no evidence of a positive correlation between the amount of insurance and nursing home admission rates; indeed, there is even a pronounced negative correlation between admission rates and some of the policy features that increase the amount of insurance. Although suggestive, the SOA data do not provide a formal test of the positive correlation prediction. Most importantly, they do not condition on the risk classification of the individuals done by the insurance companies. In addition, many uninsured individuals may in fact be able to collect public Medicaid insurance should they end up in a nursing home. Our formal analysis of micro data in the remainder of this section is designed to address these issues. We perform the test in two different ways. Our first comparison is to compare care utilization across insured individuals with different amounts of insurance. To do so we use a proprietary database containing information on the insurance purchases and subsequent claims experiences of customers in a large, private long-term care insurance company. Our second approach is to compare the care utilization 8 When the market began in the early 1980s, most policies covered nursing homes only. Even in 1990, two-thirds of policies sold covered only nursing homes. By 2000, however, over three-quarters of new policies covered both home care and nursing home care (AARP 2002, SOA 2002, HIAA 2000a). 9 We limit the insured data to policies with no deductible. Policies with a deductible will not report a claim (and hence a nursing home admission) if the nursing home stay lasts less than the length of the deductible; we would therefore underestimate the insured admission rate for these policies. 10

12 of individuals with private insurance to that of individuals without private insurance. For this analysis, we use individual-level panel survey data from the AHEAD. 3.1 Proprietary policyholder data from a large private insurance company Data and empirical framework: We have data on the complete set of individual (non-group) private long-term care insurance policies sold by a large U.S. private long-term care insurance company from January 1, 1997 through December 31, We observe a complete description of the features of each policy. Crucially, we also observe the risk classification of the individual done by the insurance company; it follows typical industry practices. The company varies the premium based on the individual s age at the time of policy issue, the date that the policy is issued, and whether the individual is rated preferred, standard, or substandard based on detailed health information. We observe the individual s age at purchase, issue date, and rating category, although we do not observe the underlying health information on which the rating category is determined. We also observe a complete description of all claims incurred through December 31, To test the positive correlation prediction, we examine the relationship between the characteristics of the policy that affect the quantity of insurance provided and nursing home utilization. In contrast to the comparison using the SOA data we employed earlier, here we can condition on the individual s risk classification. However, because we still only observe care utilization if it results in a claim, we will miss stays that do not exhaust the deductible (which must be satisfied anew for each care episode). Therefore, we define a failure in our hazard model as having at least 100 continuous days of nursing home care and we restrict the sample to the 94% of policies that have a deductible of 100 days or less (and were issued at least 100 days before the end of the sample period). Conditional on entering a nursing home, stays of more than 100 days are quite common (Dick et al., 1994; Kemper and Murtaugh, 1991; and 10 The company is among the top-five companies in this market (which combined account for almost two-thirds of premiums (LIMRA, 2001) ). Although the data come from a single company, they appear comparable to the broader market in terms of the age and gender-mix of purchasers and the product mix of policies sold (see HIAA 2000a for market-wide statistics). In addition, the company experienced similar growth rates in policy sales over the last five years to the industry as a whole (LIMRA 2001). 11

13 Murtaugh et al., 1997). The average failure rate in our sample, 0.3 percent, is quite low, but is consistent with market-wide and population statistics on nursing home utilization (SOA 1992, 2002). 11 Let λ t, x, β, λ ) denote the hazard function, the probability that a policyholder with personal and ( i 0 policy characteristics x i enters their 100 th day of continuous nursing home care t days after purchasing the policy, conditional on not having done so prior to t. We use the standard proportional hazard model which assumes that λ t, x, β, λ ) can be decomposed into a baseline hazard λ ( ) and a proportional ( i 0 shift factor exp( x β ) as follows: i (1) λ t, x, β, λ ) = exp( x β ) λ ( ). ( i 0 i 0 t We estimate a semi-parametric Cox proportional hazard model to avoid making any parametric assumptions about the baseline hazard λ ( ). 0 t The hazard model framework is particularly well-suited to handling the extensive right-censoring in the data. Censoring (exiting the sample for reasons other than failure) occurs either because the sample period ends or because the policy terminates due to death or to failure to pay premiums. Slightly less than 10 percent of our policies terminate; this rate is comparable to industry-wide termination rates (SOA 2002). 12 We include a set of covariates to control for the insurance company s risk classification of the individuals. These consist of indicator variables for issue year, rating category (standard, preferred or substandard), and issue age (which we divide into five roughly equal size bins that are less than 60, 60-64, 65-69, 70-74, and 75+). 13 Finkelstein and Poterba (forthcoming) show that selection can occur on many aspects of the insurance 0 t 11 This low failure rate prohibits an analysis of the relationship between policy characteristics and length of stay beyond 100 days, or the occurrence of multiple stays of at least 100 days in length. 12 Treating terminated policies as censored at the date of termination is equivalent to a competing risks framework in which the two risks (termination and failure) are assumed independent. It is not obvious that this assumption is appropriate. We therefore tested the robustness of our results to instead maintaining the terminated policies in the at risk sample after policy termination. The results were not substantively affected. 13 Including separate indicator variables for each age rather than five-year intervals does not affect the coefficients of interest. We adopt the coarser set of controls as our main specification simply for ease of presentation. 12

14 contract. In testing for the positive correlation property, it is therefore important to look at the correlation between care utilization and any aspect of the insurance policy along which selection might occur. We therefore include as our primary covariates of interest measures of all four of the main aspects of the policy that affect the quantity of insurance in the policy. These are: (1) the deductible, (2) the total number of days for which benefits may be received in the lifetime of the policy ( benefit period ), (3) the maximum amount of incurred nursing home care expenditures that the policy will reimburse per day in care ( maximum daily benefit ), and (4) how the nominal maximum daily benefit increases over time after purchase of the policy ( benefit escalation ). The positive correlation property predicts that the hazard rate should be increasing in the benefit amount, the benefit period and the amount of benefit escalation, all of which increase the amount of insurance in the contract; similarly, the hazard should be decreasing in the size of the deductible, which reduces the amount of insurance in the contract. We measure the deductible with indicator variables for 20-day, 60-day and 100-day deductibles. We measure the maximum daily benefit amount using three indicators (which roughly evenly divide the sample) for less than $100, $100, and more than $100 per day. In measuring the benefit period, we create a series of indicator variables that take account of two factors. First, we distinguish among policies with benefit periods of 1-4 years, 5+ years (but finite), and unlimited. Second, among policies with finite benefit periods, we further distinguish policies that reset the allowable benefit period to the original benefit period if the individual has had 180 continuous days out of care since the last day of receiving benefits; this reset option effectively extends the benefit period. Finally, we use indicator variables for the four possible benefit escalation options. In order of increasing benefit levels these are: constant nominal benefits, benefits escalate at 5 percent of the original benefit per year ( simple escalation), benefits escalate at 5 percent per year ( compound escalation), and benefits are increased by the greater of 5% compounded annually over 3 years or CPI-growth over the last 3 years at the option of the policy holder ( indexed ). For completeness, we also control for the remaining policy features as described in the notes to Table 2. Table 1 provides summary statistics on the main individual and policy characteristics examined in the 13

15 analysis. We do not control for the premium because we have controlled for all of the characteristics of the individual and the policy that determine it. We also do not control for sex because it is not used in determining the pricing of contracts Results: Table 2 reports the results from estimating equation (1). We show results for the entire sample of policies. Because some of these policies have been in effect for only a short time, we also report results for the subset of policies issued in 1997 or 1998, all of which have had at least three years of exposure. The results look similar if we instead limit the sample to individuals who are 75 and older at the time of purchase, and for whom we therefore observe a greater fraction of the policies actual lifetime (results not shown). The results in the top portion of the table show the estimated coefficients on several covariates that reflect the insurance company s risk-categorization of the individual. As expected, the hazard rate increases monotonically with the individual s issue age and with the assessed risk category. For example, individuals who are rated standard risk have about a 55 percent lower baseline hazard rate of entering a nursing home for at least 100 days than individuals who are rated high risk. The lower portion of the table reports the coefficients on covariates for which the positive correlation property makes predictions; these predictions are summarized in the right-most column. There is little evidence in support of these predictions. The coefficients on the benefit escalation and benefit period variables tend to have the opposite sign from what is predicted by the positive correlation property. The coefficients on the deductible and daily benefit variables tend to be positive as predicted (those with shorter deductible periods and higher daily benefits are more likely to use a nursing home) but the estimated effects are almost always statistically insignificant. Moreover, their magnitudes suggest that any effect is quantitatively unimportant. For example, the change in hazard rate associated with a 20-day deductible compared to a 100-day deductible (which is the largest right-signed coefficient) is not only statistically insignificant but is considerably smaller in magnitude than the change in hazard associated with any 5-year increase in issue age. 14

16 One potential concern with these findings is that our inclusion of a series of additive controls for the individual s risk classification may produce misleading estimates of the relationship between features of the contract and nursing home utilization if there are important interaction effects among the various determinants of the individual s risk classification and nursing home utilization. We therefore estimated a more flexibly specified version of equation (1) in which we included fixed effects for each risk class, defined by the interactions of the individual s issue age, rating category and issue year. We also reestimated the hazard model restricting our sample to an increasingly homogenous population with respect to the insurance company s risk classification. We found (in results not shown) that the coefficients on the policy characteristic variables in these alternative specifications were, if anything, less consistent with the predictions of the positive correlation property than those shown in Table Evidence from individual panel data in the AHEAD Data and empirical framework: The proprietary insurance company data provide detailed information on the relationship between the amount of insurance and subsequent claims. However, they contain no comparative information on the experience of those without private insurance. Such information is available in the Asset and Health Dynamics (AHEAD) cohort of the Health and Retirement Study (HRS). This sample, first interviewed in 1993, is representative of the non-institutionalized population born in 1923 or earlier and their spouses. Because the first wave of the survey does not provide a reliable measure of long-term care insurance coverage, our analyses begin with the second interview in 1995, at which point the average age of individuals in our sample is 79. We use the panel nature of the data to track nursing home utilization for the 1995 respondents through the latest currently available interview in Appendix A provides more detail on the sample and variable definitions. The basic estimating equation is: (2) CARE = X β 1 + β 2LTCINS + ε We regress a measure of the individual s long-term care utilization from 1995 through 2000 (CARE) on 15

17 whether he has long-term care insurance coverage in 1995 (LTCINS); 10% of the sample has such coverage. We include as controls a series of covariates (X) designed to control for any risk-categorization of the individual done by the insurance company. We use two different measures for the dependent variable CARE. The first is a binary measure of whether the individual spent any time in a nursing home in the five years between 1995 and 2000; 19 percent of the sample did. The second dependent variable is the total number of nights that the individual spent in a nursing home in this period. On average, individuals spent 33 nights in a nursing home; conditional on entering a nursing home, the mean is 187 nights. As discussed, the correct empirical test requires controlling for the risk classification of the individual done by insurance companies. In the proprietary insurance company data, we directly observed this risk classification. In the AHEAD data we do not. However, we do observe extremely rich and detailed information on current health and medical history, as well as other demographics. By examining insurance application forms from five leading long-term care insurance companies we determined which of these characteristics of the individual the insurance companies observe. All collect a limited set of demographic information age, gender, marital status, and age of spouse as well as similar and extremely detailed information on current health and on health history. We found only one company that asked applicants to report any financial information (specifically, whether they had less than $30,000 in financial assets, presumably to screen for likely Medicaid eligibility). Essentially all of the information collected by the insurance companies is observable in AHEAD. We also know that companies offer age-specific prices with only two or three broad rate classifications within each age based on health information (ACLI 2001, Weiss 2002, Kemper et al. 1995). 14 However, we do not know the algorithm mapping the observable characteristics into the rate classifications. Given the importance of controlling for the individual s risk classification in the analysis, we experiment with four alternative approaches. First, we do not include any covariates in estimating equation (2) ( no controls 14 According to industry actuaries, insurance companies collect more detailed information than they currently use in risk classification in order to build a detailed claims database for future improvements in actuarial modeling. 16

18 specification). Second, we control for the individual s age by including a separate indicator variable for each age ( age dummies specification). Both of these approaches are likely to underestimate the amount of categorization done by insurance companies. Therefore, our third approach ( all observables specification) tries to control for everything the insurance companies observe about the individual. This specification includes not only the age dummies, but also all of the demographic information that insurance companies observe, (gender, marital status and age of spouse, which we enter linearly), and indicator variables for each of the detailed current health and health history characteristics collected by any insurance companies that we observe in the data. To be conservative, we also include indicator variables for the household s income quartile and asset quartile, even though it appears that most companies do not collect this information. This complete set of controls is summarized in Table 3. By including a separate indicator variable for each health characteristic, the all observables specification invokes a much more finely defined categorization of risk than insurance companies actually use. We therefore believe that this specification is likely to overestimate the amount of risk classification done by the insurance company. 15 However, if there are substantial interaction affects among the observable controls, we may misestimate the true relationship between care utilization and insurance coverage by only including these observable controls additively. To address this limitation, our fourth and final specification substitutes these linear controls with a single summary measure of the insurance companies prediction about each individual in the 1995 AHEAD s chance of entering a nursing home in the next five years. We generated these predictions using the same actuarial model that is employed by much of the long-term care insurance industry; this model and its pedigree are described in detail in Robinson (1996), Robinson (2002), and Brown and Finkelstein 15 There are, however, a few characteristics that the insurance companies observe that we cannot measure in the AHEAD. Most are rare health conditions such as double amputation or unoperated aneurysm but their omission raises the (we think unlikely) possibility that the all observables specification underestimates the amount of risk classification done by the insurance company. To compensate for this omission, we experimented with including as controls all of the health measures observed in the AHEAD, including those not observed by the insurance company (e.g. self-reported health status, cataract surgery etc.). We did not find any substantive changes in our results. 17

19 (2003). 16 We use a version of the model that predicts care utilization for typical individuals in the population and makes no adjustment for potential moral hazard effects of the insurance. The predictions depend non-parametrically on the individual s age, gender and membership in one of seven different health states (defined by the number of limitations to instrumental activities of daily living (IADLs), the number of limitations to activities of daily livings (ADLs), and the presence or absence of cognitive impairment); all of this information is available in the AHEAD. 17 This measure provides a parsimonious way of controlling for non-linear (and non-parametric) interactions between the observed characteristics of the individual and nursing home utilization Results: The top panel of Table 4 describes the results of estimating equation (2) for these four alternative definitions of the control variables (X). When the dependent variable is the binary measure of any nursing home use, we report results from OLS estimation of equation (2); probit estimation produces similar results. When the dependent variable is the cumulative number of nights spent in a nursing home since 1995, we report estimates from a Tobit model; a linear model produces similar results both for the whole sample and when limited to those who report any time in a nursing home. The results are not supportive of a positive correlation between long-term care insurance coverage and long-term care utilization. In all specifications, long-term care insurance coverage is negatively associated with long-term care utilization. Across all specifications, we can reject a higher probability of nursing home utilization for the insured relative to the uninsured of more than 2.8 percentage points (15 percent) with 95 percent confidence. A potential problem with this analysis is that a substantial fraction of the seemingly uninsured may in 16 We are extremely grateful to Jim Robinson, the former chair of the Society of Actuaries long-term care insurance valuation methods task force, for generously sharing this model with us, and for answering our many questions. 17 Although the full model, which is what we use, generates separate predictions by gender, in practice insurance companies do not offer gender-specific prices. If we instead generate the unisex predictions of the model, we find that it performs equally well in predicting nursing home utilization, and that conditional on this unisex actuarial prediction, gender is not a statistically significant predictor of nursing home use in the AHEAD. These findings are consistent with insurance companies not offering gender-specific prices. 18 As an alternative way of dealing with non-linearities in the relationship between observable characteristics and long-term are utilization, we also estimated equation (2) on increasingly homogenous sub-samples of individuals from the perspective of the insurance company (e.g. by age and health conditions). The results were not affected. 18

20 fact rely on the public insurance provided by Medicaid, which pays for 40% of all nursing home expenditures (US Congress, 2000). To address this issue, we repeat the regressions shown in the top panel of Table 4, restricting the sample to those individuals who are least likely to find Medicaid an attractive substitute for private insurance. Specifically, because Medicaid coverage in effect carries a deductible of almost all of one s assets and is therefore a more attractive substitute for lower-wealth individuals, we restrict the sample to individuals in the top quartile of the household income or wealth distribution in The bottom panel of Table 4 indicates that the relationship between insurance coverage and care utilization appears more negative when the sample is restricted to these individuals. Indeed, across all specifications, we can now reject a higher probability of nursing home utilization for the insured relative to the uninsured of more than 0.6 percentage points (3 percent) with 95 percent confidence. In results not reported, we ascertained that the results in Table 4 were robust to a number of other alternative specifications. Two in particular are worth noting. First, insurance companies tend to deny some observably unhealthy individuals private long-term care insurance coverage; for example, Weiss (2002) estimates that 15% of non-group long-term care insurance applications are denied. We therefore re-estimated equation (2) restricting the sample to individuals who have none of the health conditions that tend to provoke denials. The coefficient on long-term care insurance remains consistently negative, even if the sample is further restricted to those for whom Medicaid is also not a close substitute for private insurance. 19 Second, because we only observe care utilization for a five-year period, and not over the lifetime of the policy, it is possible that the positive correlation property would appear if the data were analyzed over a longer time horizon. We tried several alternative approaches to addressing this issue, none of which affected the qualitative nature of the results. For example, we used information on how long the individual has had his policy to restrict the insured individuals in the sample to the two-thirds who had 19 We verified that the results presented in the remainder of the paper were also not substantively affected by limiting the sample to the top quartile of the income or wealth distribution, or to individuals unlikely to be denied insurance, although in some specifications the standard errors increased so that the results in these smaller samples were no longer statistically significant. 19